The 1-0 reverse was Genoa's first loss at home since September and dropped the Grifoni to 11th place in the Serie A standings.
"We had our chances to score and we didn't take them," Gasperini said. "It's disappointing to lose a derby, especially when we played well.
"We didn't deserve to lose and we left the game with our heads held high.
"This disappointment must give us the determination to hit back and take three points at Livorno."
The Grifoni will need to show a vast improvement if they are to clinch their first win on the road since early November.
Gasperini's men have collected only three points - all from draws - since then on their travels.
"We need to improve our performances away from home," Gasperini said. "We already showed an improvement in Florence (a 3-3 draw at Fiorentina) and now we must try to take three points in Leghorn."
Genoa striker Alberto Gilardino, who has scored one goal in his team's last four league games, will lead the visitors' attack.
Livorno have warned their opponents to expect a battle.
The Amaranto followed their 3-1 win over Sassuolo with a 3-3 draw at Catania last time out.
The result left the Tuscan outfit in 18th place, just one place and one point adrift of Bologna, who hold the last position of safety.
"If we want to defend our Serie A status we have to take points against any rivals," Livorno coach Domenico Di Carlo said.
"I see my players very motivated and determined to achieve our aim which is to avoid the drop."
The hosts will be without forward Luca Siligardi, who sustained an ankle injury last weekend and will be sidelined for a month, while defender Ibrahima Mbaye serves a one-match ban.